Data collected from supermarket checkout counters can be used to evaluate the effect of price on the sales of any product. Weekly data was collected on a particular beverage brand, including sales (y, in number of units) and price (x, in dollars) from 8 stores. In the sample data, r has a sample mean of 20 and a sample standard deviation of 2, while y has a sample mean of and a sample standard deviation of The sample correlation between r and y is -0.8. S 172 (1) Compute the simple linear regression equation (2) Carry out a test at significance level 0.01 to decide whether there is a linear rela- tionship between r and y. Your conclusion should be based on a P-value. You may use bounds for the P-value. (3) Would the conclusion of (2) have changed if you had tested appropriate hypotheses to decide whether there is a negative linear association in the population? Explain.

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Data collected from supermarket checkout counters can be used to evaluate the effect of
price on the sales of any product. Weekly data was collected on a particular beverage
brand, including sales (y, in number of units) and price (r, in dollars) from 8 stores. In
the sample data, r has a sample mean of 20 and a sample standard deviation of 2, while y
has a sample mean of and a sample standard deviation of 9 The sample correlation
between r and y is -0.8. 172
(1) Compute the simple linear regression equation
(2) Carry out a test at significance level 0.01 to decide whether there is a linear rela-
tionship between z and y. Your conclusion should be based on a P-value. You may
use bounds for the P-value.
(3) Would the conclusion of (2) have changed if you had tested appropriate hypotheses
to decide whether there is a negative linear association in the population? Explain.
(4) How would the estimates of Bo, B1, and o change if n > 8? Explain.
Transcribed Image Text:Data collected from supermarket checkout counters can be used to evaluate the effect of price on the sales of any product. Weekly data was collected on a particular beverage brand, including sales (y, in number of units) and price (r, in dollars) from 8 stores. In the sample data, r has a sample mean of 20 and a sample standard deviation of 2, while y has a sample mean of and a sample standard deviation of 9 The sample correlation between r and y is -0.8. 172 (1) Compute the simple linear regression equation (2) Carry out a test at significance level 0.01 to decide whether there is a linear rela- tionship between z and y. Your conclusion should be based on a P-value. You may use bounds for the P-value. (3) Would the conclusion of (2) have changed if you had tested appropriate hypotheses to decide whether there is a negative linear association in the population? Explain. (4) How would the estimates of Bo, B1, and o change if n > 8? Explain.
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